A conventional quantum cryptosystem is described below. Recently, optical communications, which allow high-speed, large-capacity communication, have been widely used. In such an optical communication system, the communication is performed by turning a light beam on and off. When the light beam is turned on, a large quantity of photons are transmitted, so that such optical communication system does not directly produce the quantum effect.
On the other hand, in the quantum cryptosystem, the photon is used as a communication medium, and information of one bit is transmitted by one photon so that the quantum effect such as the uncertainty principle is generated. If a person who wants to tap the communication (hereinafter, “interceptor”) randomly selects a base to measure the photon without knowing a quantum state such as a phase, the quantum state is changed. Therefore, on a receiver side, it is possible to recognize whether transmission data is intercepted by confirming the change in quantum state of the photon.
FIG. 9 is an overview of a conventional quantum key distribution utilizing polarization. For example, a measuring apparatus, which can identify the light polarized in a horizontal direction from the light polarized in a vertical direction, correctly identifies the light polarized in the horizontal direction (0°) on a quantum communication path from the light polarized in the vertical direction (90°) on the quantum communication path. On the other hand, another measuring apparatus, which can identify the light polarized in an oblique direction (45°, 135°), correctly identifies the light polarized in the oblique direction of 45° on a quantum communication path from the light polarized in the oblique direction of 135° on the quantum communication path.
As described above, each measuring apparatus can correctly recognize the light polarized in the specified direction. However, when the light polarized in the oblique direction is measured with the measuring apparatus that can identify the light polarized in the horizontal direction from the light polarized in the vertical direction, the apparatus recognizes the light polarized in the horizontal direction (0°) and the light polarized in the vertical direction (90°) with the probability of 50% respectively. Namely, when a measuring apparatus that does not match the identifiable polarized direction is used, even if the measurement result is analyzed, the polarized direction cannot be correctly identified.
In the quantum key distribution shown in FIG. 9, by utilizing the uncertainty (randomness), a person who transmits the data (transmitter) and a person who receives the data (receiver) share a key without being known by the interceptor (Patent Literature 1). The transmitter and the receiver can also use a public communication path in addition to the quantum communication path. A procedure of sharing the key is described.
The transmitter first generates a random number sequence (sequence of 1 and 0: transmission data) and randomly chooses a transmission code (+: the code corresponding to the measuring apparatus that can identify the light polarized in the horizontal direction from the light polarized in the vertical direction, and ×: the code corresponding to the measuring apparatus that can identify the light polarized in the oblique direction). The combination of the random number sequence and the transmission code can automatically set the polarized direction of the transmitted light. In this case, the light polarized in the horizontal direction by the combination of 0 and +, the light polarized in the vertical direction by the combination of 1 and +, the light polarized in the 45° direction by the combination of 0 and ×, and the light polarized in the 135° direction by the combination of 1 and × are transmitted to the quantum communication path (transmission signal).
The receiver randomly chooses a reception code (+: the code corresponding to the measuring apparatus that can identify the light polarized in the horizontal direction from the light polarized in the vertical direction, and ×: the code corresponding to the measuring apparatus that can identify the light polarized in the oblique direction) and measures the light on the quantum communication path (reception signal). The receiver obtains reception data by the combination of the reception code and the reception signal. In this case, 0 is obtained as the reception data by the combination of the light polarized in the horizontal direction and +, 1 is obtained as the reception data by the combination of the light polarized in the vertical direction and +, 0 is obtained as the reception data by the combination of the light polarized in the 45° direction and ×, and 0 is obtained as the reception data by the combination of the light polarized in the 135° direction and ×.
The receiver then transmits the reception code to the transmitter through the public communication path in order to check whether the receiver has performed a measurement with an appropriate measuring apparatus. Having received the reception code, the transmitter checks whether the measurement of the receiver has been performed with an appropriate measuring apparatus. The transmitter transmits the result to the receiver through the public communication path.
The receiver then saves (keeps behind) only the reception data corresponding to the reception signal which is received with the appropriate measuring apparatus, and discards other pieces of the reception data. At this point, the transmitter and the receiver can securely share the saved reception data.
The transmitter and the receiver then transmit the predetermined number of pieces of data selected from the common data to each other through the public communication path. The transmitter and the receiver confirm whether the received data corresponds to the data owned by oneself. For example, when even one piece of the confirmed data does not correspond to the data owned by the transmitter or the receiver, judging that the interceptor is present, they discard the common data and perform the process of sharing the key again from the start. On the other hand, when the confirmed data completely corresponds to the data owned by the transmitter or the receiver, judging that there is no interceptor, the transmitter and the receiver discard the data used for the confirmation, and the saved common data becomes the common key for the transmitter and the receiver.
Application of the conventional quantum key distribution method includes the quantum key distribution method that can correct data error on a transmission path.
In the method, in order to detect the data error, the transmitter divides the transmission data into a plurality of blocks and transmits parity in each block onto the public communication path. The receiver compares the parity in each block received through the public communication path, to the parity of the corresponding block in the reception data and checks the data error. When a different parity is present, the receiver transmits a reply of the information indicating which parity of the block is different onto the public communication path. The transmitter further divides the appropriate block into a first half block and a second half block and transmits, for example, the first half parity onto the public communication path (binary search). The transmitter and the receiver then specify a position of an error bit by repeating the binary search, and the receiver finally corrects the specified bit.
Assuming that it is determined that a parity is correct due to even number of errors even if an error is present in the data, the transmitter randomly permutates the transmission data (random permutation) to divide the transmission data into a plurality of blocks and performs the error correction processing by the binary search again. All the data errors are corrected by repeatedly executing the error correction processing by the random permutation.
Patent Literature 1: Bennett. C. H. and Brassard, G.: Quantum Cryptography: Public Key Distribution and Coin Tossing, In Proceedings of IEEE Conference on Computers, System and Signal Processing, Bangalore, India, pp. 175-179 (DECEMBER 1984).
Patent Literature 2: Brassard, G. and Salvail, L. 1993 Secret-Key Reconciliation by Public Discussion, In Advances in Cryptology—EUROCRYPT '93, Lecture Notes in Computer Science 765, 410-423.
In the conventional quantum key distribution shown in FIG. 9, however, an error communication path is not considered. When an error is present, the common data (common key) is discarded because an intercepting action is presumed to be present. Therefore, there is a problem that creation efficiency of the common key is correspondingly affected in some transmission paths.
In the quantum key distribution method that can correct the data error on the transmission path, huge number of exchanges of the parity is generated for specifying the error bit, and the error correction processing is also performed in a predetermined times by the random permutation. Therefore, there is a problem that a long period of time is required for the error correction processing.
It is an object of the present invention to provide a quantum key distribution method that can create a highly-secured common key while correcting data error on a transmission path by an error correction code having remarkably high characteristics.